2.The diagram below shows the trajectories of three charged...

2.The diagram below shows the trajectories of three charged particles moving in a uniform magnetic field of strength B. The field points into the plane of the paper. The particles are moving in the plane of the paper. The direction in which each particle is moving is shown by the arrows. (a) For each particle, find if the charge is positive or negative (Q>0 or Q<0). Q1: Q2: Q3: (b) Assume all particles have the same velocity (v) and the same charge charge magnitude |Q|. Which particle will have the greater mass? Explain your answer in a couple of sentences. Derive the formula you used to answer this question. Will the speed of the particles change as they move in the magnetic field? (c) For each of the curves below pick a point in the trajectory and indicate the velocity vector at that point and the direction of the force due to the magnetic field.

Transcript

00:01 Hello guys.

00:02 So for the given question we have been given three charge particles.

00:06 Q1, q2 and q3 are moving in a uniform magnetic field having strength b and lying in the plane of paper.

00:15 We need to find the nature of charge on each particle.

00:19 For part a, for part b of the question, we have been given that if particles have same velocity and same charge, then which will have a greater mass.

00:30 And for part c of the question, we need to find.

00:32 A point on the trajectory of each curve and indicate the velocity vector and force acting due to magnetic field.

00:43 So for the solution of part a of the problem, we need to understand the force acting on the particle, charged particle moving in a uniform magnetic field.

00:53 So force acting on a charged particle moving in an uniform magnetic field is denoted by f -benacted.

01:29 And the value of f vector is given by the formula charge q multiplied with the cross product of velocity vector with magnetic field vector.

01:44 So the motion of any charge particle in a uniform magnetic field is dependent on the cross product of velocity vector v with magnetic field vector b and the direction of which is given by the right hand thumb rule according to which if we stretch the palm of our right hand in the direction of velocity vector and curled the fingers in the direction in the direction magnetic field vector then the thumb of right hand will point towards the direction of force acting on the particle alright so from here for particle one we can say its velocity vector is along positive x -axis and magnetic field vector is towards the z negative axis so by applying right -hand thumb rule we can say the force vector will act along negative y axis so particle 1 or q1 is positive as it is rotating in clockwise direction as it is rotating in clockwise direction similarly for particle 2 velocity vector is is along x positive direction magnetic field vector is along z negative direction force will act along y negative direction or y negative axis hence q2 is positive as it is also rotating in clockwise direction for particle 3 velocity vector is along x negative direction magnetic field vector is along z negative direction so force vector should be along y positive direction but here it is acting in opposite direction so charge on particle q3 should be negative.

08:39 So this is the solution for part a of the problem.

08:49 It is given that if the particles have same charge and same velocity, then which particle is heavier than the others.

08:57 So as the particles are moving in a circular motion, so we can write force is a equal to m v square divided by r where m is the mass v is the velocity and r is the radius of circular path which is also equal to q v b multiplied with sine of angle theta here theta is the angle between velocity vector and magnetic field vector here as the velocity vector and magnetic field vector are lying in the mutually perpendicular directions.

09:49 So, theta will have the value equals to 90 degree.

09:55 So centrifugal force mv squared divided by r will be equals to qvb.

10:08 So from here we can write the value of r to be equals to mv divided by qb.

10:22 So this is the formula we use to determine the value of mass...

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